A numerical study of stiffness effects on some high order splitting methods

In this paper we compare operator splitting methods of first, second, third and fourth orders that are applied to problems with stiff matrices.In order to efficiently solve the resultant subproblems is necessary to use implicit Runge-Kutta methods. It is known that, in this context, the precision or...

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Detalles Bibliográficos
Autores: J. Salcedo-Ruiz, F. J. Sánchez-Bernabé
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2006
País:México
Institución:Universidad Autónoma Metropolitana
Repositorio:Redalyc-UAM
OAI Identifier:oai:redalyc.org:57065005
Acceso en línea:https://www.redalyc.org/articulo.oa?id=57065005
Access Level:acceso abierto
Palabra clave:Física, Astronomía y Matemáticas
stiff matrix
Kutta methods
implicit Runge
Operator splitting
Richardson extrapolation
Descripción
Sumario:In this paper we compare operator splitting methods of first, second, third and fourth orders that are applied to problems with stiff matrices.In order to efficiently solve the resultant subproblems is necessary to use implicit Runge-Kutta methods. It is known that, in this context, the precision order of operator splitting schemes is reduced. Furthermore, we propose a fifth order operator splitting method that is obtained by applying Richardson extrapolation to a fourth order method. All methods are tested with a model problem with matrices such that its condition number is taken up to 20,000. Our conclusion is that order reduction is more severe for low order operator splitting methods.